Seismic prospecting entails generating elastic waves in a subterranean formation through artificial means and analyzing the response from the formation to describe the properties of the formation. Seismic prospecting is characterized by three stages: data acquisition; data processing; and data interpretation. To initiate data acquisition, a seismic source generates a seismic wave that propagates into the earth and is, at least partially, reflected by subsurface seismic reflectors. The reflected signals are then recorded by seismic receivers or receiver arrays that are positioned at various locations relative to the seismic source. The recorded seismic data are referred to as seismic data traces, which represent the response of an elastic wavefield to velocity and density constraints across interfaces of rock or sediment. The seismic data trace may contain a plurality of reflected signals received from the formation. Typically, the retrieved seismic data traces are processed further into a form that is better suited for interpretation. Interpretation of the processed seismic data can yield valuable information on the subterranean formations.
A seismic data trace is represented in a computer as a float point data array. The numbers in the data array are equal interval amplitude samples. Thus, if the sample interval is 2 ms, a one second long seismic data trace will have 500 samples. The graph 10 shown in FIG. 1 is an example of a recorded seismic data trace, T. The numbers, N on each side, show the recording time starting from zero to more than one second. The shaded portion of the recorded data trace, on the right side shows the positive amplitude and the unshaded area on the left side shows the negative amplitude. Seismic data traces typically contain both the desired seismic reflections and one or more unwanted noise components, including various velocity ground roll noises and low or high frequency noises. It is generally known that these noises can overwhelm the desired seismic reflections and reduce the accuracy of interpretation based on the seismic data traces. Accordingly, improved methods for attenuating noise components so as to obtain seismic data traces that more accurately reflect properties of the target subterranean formation are particularly desirable.
One conventional method for attenuating unwanted noise components in seismic data traces may be referred to as a common-midpoint (CMP) stacking method (the “CMP” method). The “midpoint” for a seismic data trace is the point located midway between the source location and the receiver location for that trace. According to the CMP method, seismic data traces are recorded for multiple source-receiver pairs. The recorded seismic data traces are sorted into common-midpoint gathers or collections of seismic data traces having the same midpoint but different source-to-receiver offset distances. The seismic data traces within each CMP gather are first corrected for static and normal moveout. The corrected seismic data traces are then summed or “stacked” to yield a stacked data trace that is a composite of the individual seismic data traces in the CMP gather. Before “stacking”, the individual seismic data traces are referred to as pre-stack seismic data traces. After stacking, the summed or stacked data traces are referred to as post-stack seismic data traces. Typically, a post-stack seismic data trace exhibits a significantly improved signal-to-noise ratio compared to a pre-stack seismic data trace.
Both types of seismic data traces can be divided into wavelets that are reflected from petrophysical or lithological boundaries or reflectors in the subsurface at different depths. A seismic wavelet or an embedded wavelet is defined as a seismic pulse usually consisting of only a few cycles. An embedded wavelet or basic wavelet is the time domain reflection shape from a single positive reflector at normal incidence. A wavelet may be defined by its amplitude and shape. The amplitude may be a constant or a variable of a positive or negative real number. The shape of the wavelet may be described by a mathematical function or time series of amplitude samples. Seismic data traces may also contain noise that can be separated or divided into the form of wavelets. As described in the Detailed Description of Preferred Embodiments, “modified” seismic data traces may be generated using wavelets derived from originally recorded seismic data traces or from processed seismic data traces to yield seismic data that more accurately reflect the properties of the target subterranean formation.